The present invention relates to a method and apparatus for analyzing heart-rate variability of an object to be examined on the basis of electrocardiogram information acquired from the object, and a computer-readable program for a computer to analyze the heart-rate variability of the object.
Recently, an analysis on heart-rate variability of an object to be examined has been spotlighted in many fields, such as sports medical check, and health check. This analysis has been known as “heart-rate variability analysis.”
One technique for conventional heart-rate variability analysis is proposed as a CDM (Complex Demodulation) technique, which is pictorially illustrated in FIG. 1. As shown in FIG. 1, electrocardiogram information acquired from an object, which is measured by an electrocardiogram measuring device 1, is fed to a peak-to-peak interval detector 2, where a peak to peak interval of an electrocardiogram waveform is detected and data indicative of the peak to peak interval is calculated. The resultant peak-to-peak interval data is fed to a modulator 4, to which sinusoidal waves of 0.3 Hz are also supplied from a sinusoidal-wave generator 3, so that the modulator 4 multiplies the peak-to-peak interval data by the sine wave and the cosine wave to generate intermediate frequency quadrature signals I (In-phase) and Q (Quadrature).
The quadrature signals I and Q are then sent to a demodulator 5, where those signals I and Q are subjected to low-pass filtering at a bandwidth of 0.15 Hz, so that the signals I and Q are demodulated. Based on the demodulated results, a heart-rate fluctuation output device 6 outputs pieces of information indicating fluctuations in the heart rate of the object.
The fluctuations in the heart rate indicate an index of heart-rate variability. The heart-rate variability shows variations in the cardiac cycles attributable to fluctuations in automatic nerve input to the sinoatrial nodes. In general, to analyze the heart-rate variability requires that peak to peak intervals (hereinafter, called RR intervals) in an electrocardiogram waveform be measured.
A mathematical approach to calculating the amplitude of a breathing component included in the heart-rate fluctuations based on the CDM technique will now be described.
It is assumed that a breathing frequency is fr, a phase is φ, and an intermediate frequency is fw. A signal indicating RR intervals affected by the heart-rate fluctuations is expressed by the following formula:y=A*sin(2π*fr*t+φ),wherein A denotes the amplitude of a breathing component of a heart-rate fluctuation signal, fr denotes a breathing frequency, and t denotes the time.
Local signals generated from the sinusoidal-wave generator 3 can be expressed as follows:sin(2π*fw*t) and cos(2π*fw*t).
Multiplying the RR interval signal by the local signals at the modulator 4 produces intermediate frequency signals I and Q, which can be expressed as follows:I=y*sin(2π*fw*t)=sin(2π*fr*t+φ)*A*sin(2π*fr*t) andQ=y*cos(2π*fw*t)=sin(2π*fr*t+φ)*A*cos(2π*fw*t).
Using the production relations of trigonometric functions:sin(x)*sin(y)=1/2*(cos(x−y)−cos(x+y)) andcos(x)*sin(y)=1/2*(sin(x−y)−sin(x+y)),The above formulas can be written into:I=1/2*A*(cos(2π*fw*t+φ−fr*2π*t)−cos(2π*fw*t+φ+fr*2π*t) andQ=1/2*A*(sin(2π*fw*t+φ−fr*2π*t)−sin(2π*fw*t+φ−fr*2π*t)
The breathing frequency fr is usually in a range of 0.15 to 0.45 Hz. Thus, if the local signal fw from the sinusoidal-wave generator 3 is 0.3 Hz, the calculation of fw−fr produces an amount of −0.15 Hz to +0.15 Hz, while the calculation of fw+fr produces an amount of 0.45 Hz to 0.75 Hz. This means that it is sufficient that the demodulator 5 has a low-pass filter of which passing bandwidth is 0 to 0.15 Hz and of which cutoff bandwidth is 0.45 to 075 Hz.
Applying a low-pass filter of which passing bandwidth is 0 to 0.15 Hz to the intermediate frequency signals I and Q allows the second terms of the above I and Q formals to be deleted, so that signals IX and QX are produced as follows:IX=1/2*A*(cos(2π*(fw−fr)t+φ) andQX=1/2*A*(sin(2π*(fw−fr)t+φ).
Since a trigonometric formula of:sin(x)*sin(x)+cos(x)*cos(x)=1can be used, so that a formula of:(IX)2+(QX)2=(1/2*A)2is established. Hence,A=2*((IX)2+(QX)2)0.5is obtained.
FIG. 2 shows various waveforms of signals obtained on the conventional CDM technique. As shown in FIG. 2(A), it is supposed that an input signal indicating the heart-rate variability can be expressed by a sine wave signal of which amplitude is 1 and of which frequency is 0.2 Hz. FIG. 2(B) shows the foregoing 0.3 Hz local signals, whilst FIG. 2(C) shows intermediate frequency signals (I, Q) produced by multiplying the input signal by the local signals.
Further, FIG. 2(D) shows signals (IX, IQ) produced by applying the low-pass filter to the intermediate signals (I, Q), and FIG. 2(E) shows an amplitude component signal calculated based on the low-pass-filtered signals (IX, IQ).
FIG. 3 explains the relationship between a conventional signal component and aliasing noise. As shown in FIG. 3, since the breathing frequency fr is 0.15 to 0.45 Hz and the local signal frequency fw from the sinusoidal-wave generator 3 is 0.3 Hz, the signal ranges from 0 to 0.15 Hz and the aliasing noise is in a range of 0.45 to 0.75 Hz. The low-pass filter to remove this aliasing noise has a low-passing characteristic shown by a dotted line in FIG. 3, in which a passing bandwidth is set to 0.15 Hz and a cutoff bandwidth is set to a range of 0.45 to 0.75 Hz.
FIGS. 4A and 4B show the amplitude and phase characteristics of an actually used conventional low-pass filter. As shown in FIGS. 4A and 4B, an attenuation amount at a cutoff frequency is set to about −22 dB.
As described above, the conventional heart-rate variability analysis based on the CDM technique uses a low-pass filter of which passing bandwidth is 0.15 Hz and of which cutoff bandwidth is 0.45 to 0.75 Hz. That is, since the passing bandwidth of the low-pass filter is as large as 0.15 Hz, ripple noise has frequently been superposed on the amplitude signal, as shown in FIG. 2(E). There is therefore a drawback that signal components other than a frequency indicative of the breathing are mixed, as noise, with the amplitude signal.
Further, when the breathing is disturbed, the conventional heart-rate variability analysis is likely to be affected easily by invasion of non-stationary noise, thus causing a problem that there is more noise due to frequencies other than the breathing frequency. Still further, in such a case, there has been provided no mans for detecting the breathing disturbance, so that it has been impossible to estimate reliability of calculated heart-rate variably.
In addition, the conventional heart-rate variability analysis has encountered another problem that, as understood from FIGS. 4A and 4B, the low-pass filter has no sufficient attenuation in its cutoff frequencies.